Method for measuring digging position

ABSTRACT

The invention offers a position determining method that ensures high reliability in the determination of a digging position by sensing on the ground an AC magnetic field generated by a coil housed in a digging head, even in the presence of a noise magnetic field affecting the position determination. This is a digging position determining method in a non-open-cut method of excavation which senses the AC magnetic field provided from a magnetic field source by an above-ground magnetic sensor to calculate the position of the magnetic field source from the magnitude and direction of the sensed AC magnetic field. When a noise magnetic field is generated by a nearby current in addition to a signal magnetic field generated by the magnetic field source, the magnetic field sensed by the magnetic sensor is projected on a flat plane or straight line orthogonal to a vector-valued direction of the noise magnetic field and the projective component is used to calculate at least one of the position of the magnetic field source. the tilt angle of the magnetic field source that is its inclination to tie vertical direction, and the azimuth direction of the magnetic field source that is its axial direction in a horizontal plane.

BACKGROUND OF THE INVENTION

[0001] 1. Technical Field of the Invention

[0002] The present invention relates to a method for determining thedigging position in a non-open-cut method of excavation and, moreparticularly, to a method which ensures accuracy in determiningpositions by lessening the influence of a noise magnetic field offrequency components close to that of the signal magnetic field to bemeasured.

[0003] 2. Prior Art

[0004] A horizontal drilling method, which is one of the non-open-cutmethods of this kind, uses a small-diameter pipe of 100 mm or lessacross for horizontally digging in the ground, and accordingly, such aprecision position determining apparatus as used in an ordinarysmall-diameter driving method of excavation cannot be placed near adrill. To solve this problem, it is customary in the art to adopt amethod in which an AC magnetic field is generated by a coil mounted inthe drill head and detected by an above-ground magnetic sensor like acoil to determine the current digging position.

[0005] This method is simple and easy, but since the magnetic field bythe coil is a dipole magnetic field, it rapidly attenuates with distancefrom the coil. Hence, this method has a defect of inability to achievehigh-reliability determination of the digging position when a power lineor similar magnetic noise source is present in the vicinity of the placewhere to perform the position determination.

SUMMARY OF THE INVENTION

[0006] An object of the present invention is to provide a positiondetermination method that permits high-reliability determination of thedigging position by detecting on the ground the AC signal magnetic fieldprovided from a coil housed in the drill head even if a noise magneticfield is present which affects the position determination .

[0007] To attain the above object, a digging position determining methodaccording to the present invention for non-open-cut excavation, whichsenses an AC magnetic field provided from a magnetic field source by amagnetic sensor provided on the ground and calculates the position ofthe magnetic field source from the magnitude and direction of the sensedmagnetic field, said method having a construction characterized in that

[0008] In case where in addition to a signal, magnetic field generatedby said magnetic field source, there exists a noise magnetic fieldgenerated by a nearby current,

[0009] at lease one of the position of said magnetic field source, thetilt angle of said magnetic field source to the vertical direction andthe azimuth angle of its axial direction of said magnetic field sourcein a horizontal plane is calculated, from a projective component of themagnetic field sensed by said magnetic sensor and projected on a planeor straight line orthogonal to a vector-valued direction of said noisemagnetic field.

[0010] That is, in 1999 year's investigation and research relating touseful utilization techniques of energy resources: entitled “Researchfor low-loss energizing techniques in establishment of advancedtelecommunication network”,(executed by Composite Development System forNew Energy Industrial Technique), it is described that external noisemagnetic fields, which affects the position determination in thenon-open-cut method of excavation, is mostly generated by a current ofsome kind. In this case, the magnitude of the noise magnetic fieldvaries irregularly with time, but its vector-valued direction isconstant at each field sensing position.

[0011] The present invention attains its object through the adoption ofthe following steps (A) and (B).

[0012] (A) The direction of the noise magnetic field is detected, and asensed magnetic field in which the noise magnetic field and a signalmagnetic field are mixed is projected on a plane or straight lineorthogonal to the direction of the noise magnetic field to obtain aprojective component.

[0013] Since the projective component is theoretically free from acomponent derived from the noise magnetic field, at lease one of theposition, azimuth angle and tilt angle of the magnetic field source iscalculated so that the magnitude of the projective component (in thecase of projection on the straight line) or it magnitude and direction(in the case of projection on the plane) is substantially equal to atheoretically calculated value of a corresponding quantity of a magneticfield generated from a magnetic field source, or, has a minimumdifference between the former and the latter. The sensed magnetic fieldis obtained by sensing magnetic fields at different positions whosenumber is determined by how many ones of the position, azimuth angle andtilt angle of the magnetic field source are unknowns and how suchunknowns are calculated.

[0014] (B) To obtain the noise magnetic field,

[0015] a) When the number of noise magnetic fields is virtually one:

[0016] The noise magnetic field is sensed to obtain its directionessentially in the absence of a signal magnetic field.

[0017] When the noise magnetic field has frequency components atfrequencies different from that of the signal magnetic field, thefrequency components are measured to obtain the direction of the noisemagnetic field.

[0018] b) When the number of magnetic fields is virtually two:

[0019] The frequency components of a first one of the two noise magneticfields, which are widely spaced from the frequency components of thesecond noise magnetic field and the signal magnetic field, are measuredto obtain a vector direction of the first noise magnetic field, aid thefrequency components of the second noise magnetic field, which arewidely spaced from the frequency components of the first noise magneticfield and the signal magnetic field, are measured to obtain a vectordirection of the second noise magnetic field.

BRIEF DESCRIPTION OF THE DRAWINGS

[0020] The features of the present invention will be clearly understoodfrom the following description taken in conjunction with theaccompanying drawings, in which:

[0021]FIG. 1 is a perspective view explanatory of the placement of amagnetic sensor in the present invention method;

[0022]FIG. 2 is a vector diagram explanatory of the principle ofmeasurement according to the present invention method in a case of onenoise magnetic field source;

[0023]FIG. 3 is a vector diagram explanatory of the principle ofmeasurement according to the present invention method in a case of twonoise magnetic field sources;

[0024]FIG. 4 is a flowchart illustrating a procedure for obtaining aprojective component according to the present invention method in a caseof one noise magnetic field source;

[0025]FIG. 5 is a flowchart illustrating a procedure for obtaining aprojective component according to the present invention method in a caseof two noise magnetic field sources;

[0026]FIG. 6 is a flowchart illustrating a procedure for obtaining asignal magnetic field in a case of one noise magnetic field;

[0027]FIG. 7 is a flowchart illustrating a procedure for obtaining asignal magnetic field in a case of two noise magnetic fields;

[0028]FIG. 8 is a flowchart showing a measurement procedure in thepresent invention method;

[0029]FIG. 9 is a flowchart showing a procedure for calculating theposition of the signal magnetic field according to the present inventionmethod in a case of one noise magnetic field when the number of unknownsand the number of equations are the same as to each other;

[0030]FIG. 10 is a flowchart showing a procedure for calculating theposition of the signal magnetic field source according to the presentinvention method in a case of one noise magnetic field source when thenumber of equations is larger than the number of unknowns;

[0031]FIG. 11 is a flowchart showing a procedure for calculating. theposition of the signal magnetic field according to the present inventionmethod in a case of two noise magnetic field sources when the number ofunknowns and the number of equations are the same as to each other;

[0032]FIG. 12 is a flowchart showing the procedure for calculating theposition of the signal magnetic field source according to the presentinvention method in a case of two noise magnetic field sources when thenumber of equations is larger than the number of unknowns;

[0033]FIG. 13 is a flowchart showing an example of a procedure forobtaining the signal magnetic field through the use of the magnitude ofthe signal magnetic field vector;

[0034]FIG. 14 is a flowchart showing another example of a procedure forobtaining the signal magnetic field through the use of the magnitude ofthe signal magnetic field vector;

[0035]FIG. 15 is a perspective view explanatory of the placement of amagnetic sensor for determining the direction of a noise magnetic fieldaccording to the present invention method when a digging head, which isa signal magnetic field source, is distant from the position ofmeasurement;

[0036]FIG. 16 is a flowchart showing a procedure for calculating thedirection of the noise magnetic field according to the present inventionmethod in a case where the digging head is distance from the position ofmeasurement and the signal magnetic field source stops to generate themagnetic field;

[0037]FIG. 17 is a flowchart showing a procedure for calculating thedirection of the noise magnetic field according to the present inventionmethod when the signal magnetic field and the noise magnetic field aremixed to each other;

[0038]FIG. 18 is a signal frequency spectrum diagram explanatory of howthe operation of selecting a frequency for maximizing a frequencyspectrum is used in the process for calculating the direction of thenoise magnetic field in the flowchart shown in FIG. 13;

[0039]FIG. 19 is a flowchart explanatory of a first method by which theflow of candidate vector calculating process is used in the process forcalculating the direction of the noise magnetic field in the flowchartshown in FIG. 17;

[0040]FIG. 20 is a flowchart explanatory of a second method by which theflow of candidate vector calculating process is used in the process forcalculating the direction of the noise magnetic field in the flowchartshown in FIG. 17;

[0041]FIG. 21 is a flowchart explanatory of a method by which the flowof process for evaluating the candidate vector and obtaining thedirection of the noise magnetic field is used in the process forcalculating the direction of the noise magnetic field in the flowchartshown in FIG. 17;

[0042]FIG. 22 is a signal frequency spectrum diagram explanatory of howthe operation of selecting a frequency for maximizing a frequencyspectrum is used in the process for calculating the direction of thenoise magnetic field in the flowchart shown in FIG. 13.

[0043]FIG. 23 is a signal waveform diagram explanatory of the operationof specifying a period in which only a noise magnetic field existsthrough utilization of a fact that the amplitude of the sensed magneticfield signal becomes small during the OFF period of the signal magneticfield that is turned OFF by a predetermined procedure, in thecalculation of the direction of the noise magnetic field according tothe present invention method;

[0044]FIG. 24 is a signal waveform diagram showing instantaneousvariations in the amplitude of the sensed magnetic field signal when thesignal magnetic field is periodically turned OFF in the calculation ofthe direction of the noise magnetic field according to the presentinvention method;

[0045]FIG. 25 is a signal waveform diagram showing instantaneousvariations in the amplitude of the sensed magnetic field signal when thesignal magnetic field is randomly turned OFF in the calculation of thedirection of the noise magnetic field according to the present inventionmethod;

[0046]FIG. 26 is a flowchart showing a method for calculating thedirection of the noise magnetic field according to the present inventionin which the signal magnetic field is turned OFF on the basis of apredetermined sequence, a period during which a particular magneticfield is OFF is specified by a sequence starting at the time when acorrelation function between the sequence and tile sensed magnetic fieldbecomes maximum, and the direction of the sensed magnetic field in thespecified period is regarded as the direction of the noise magneticfield;

[0047]FIG. 27 is a flowchart showing a method for calculating thedirection of the noise magnetic field according to the present inventionin which tile signal magnetic field is tuned OFF on the basis of apredetermined sequence, and the starting time of a sequence indicatingthe most likely ON/OFF state of the signal magnetic field is calculatedfrom a plurality of times when a correlation function between thepredetermined sequence and the sensed magnetic field becomes maximum;

[0048]FIG. 28 is a flowchart showing the method for calculating hedirection of the noise magnetic field according to the present inventionin which the signal magnetic field is turned OFF oil the basis of apredetermined sequence, tile correlation function between tilepredetermined sequence aid the sensed magnetic field is calculated ateach of a plurality of time points at which the period of the sequenceis equally divided, the magnetic field is projected at each time pointto a vector formed by the calculated function, aid one of vectors whosevariance is minimum is regarded as the direction of the noise magneticfield;

[0049]FIG. 29 is a flowchart showing another method for calculating thedirection of the noise magnetic field according to the present inventioni which the signal magnetic field is turned OFF on the basis of apredetermined sequence, a correlation function between the predeterminedsequence and the sensed magnetic field is calculated at each of aplurality of time points at which the period of the sequence is equallydivided the magnetic field is projected at each time point to a vectorformed by tile calculated function, and one of vectors whose variance isminimum is regarded as the direction of the noise magnetic field;

[0050]FIG. 30 is a flowchart showing the method for calculating thedirection of the noise magnetic field according to the present inventionin which the signal magnetic field is turned OFF on the basis of apredetermined sequence, and the starting time of a sequence indicatingthe most likely ON/OFF state of the signal magnetic field is calculatedfrom a plurality of time points when the correlation function betweenthe predetermined sequence and the sensed magnetic field becomesmaximum;

[0051]FIG. 31 is a flowchart showing still another method forcalculating the direction of the noise magnetic field according to thepresent invention in which the signal magnetic field is turned OFF onthe basis of a predetermined sequence, a correlation function betweenthe predetermined sequence and the sensed magnetic field is calculatedat each of a plurality of time points into which the period of thesequence is equally divided, the magnetic field is projected at eachtime point to a vector formed by the calculated function, and one ofvectors whose variance is minimum is regarded as the direction of thenoise magnetic field; and

[0052]FIG. 32 is a perspective view depicting an example of a magneticfield sensing frame for use in the present invention.

DETAILED DESCRIPTION OF THE INVENTION

[0053] As depicted in FIG. 1, in a case where the position of a digginghead 2 under the ground surface 1, which is a signal magnetic fieldsource to be sensed, is determined using a magnetic sensor 4 placed onthe ground surface 1 at a proper position when a power line or similarmagnetic noise source 3, which generates a noise magnetic field, isplaced near the digging position to be determined, there are present asignal magnetic field vector H_(s) provided from the digging head 2 anda noise magnetic field vector H_(n) from the magnetic noise source 3,such as power line. In this case, the magnetic sensor 4 senses a vectorH_(m) that is a combined version of the signal magnetic field vectorH_(s) and the noise magnetic field vector H_(n).

[0054] Now, let the noise magnetic field of a position vector r and attime t be identified as a vector H_(n)(r, t). On the other hand, let thesignal magnetic field generated by magnetic field generating means forposition sensing be identified as a vector H_(s)(r−r_(c),θ_(c), t).Here, the vector θ_(c) is an angle of orientation of the magnetic fieldgenerating means, which is defined by three angles of rotation in thecoordinate system fixed to the ground that is the coordinate systemfixed to the magnetic field generating means.

[0055] Since the noise magnetic field and the signal magnetic field areboth sensed simultaneously and since the noise magnetic field vectorH_(n)(t, t) varies randomly with time, it is impossible to extract onlythe signal magnetic field vector H_(s)(r−r_(c), θ_(c), t) from themeasured magnetic field vector H_(m)(r−r_(m), θ_(m), t) unlessstatistical properties of the noise magnetic field are known and thenoise magnetic field is signal-wise orthogonal to the signal magneticfield. Even if the statistical properties for separating the noisemagnetic field from the signal magnetic field are known prior to thedetermination of the position of the latter, the separation calls for alarge amount of data, and hence the conventional scheme is not everpractical. According to the present invention, the direction of a vectore_(n)(r) of the noise magnetic field vector H_(n)(r, t) is obtained byseparated means, and in a coordinate system shown in FIG. 2, a componentvector H_(m) ^(P)(r−r_(c), θ_(c), t), projected to a plane vertical tothe direction of a vector e_(n)(r) of the measured magnetic field vectorH_(m)(r−r_(c), θ_(c), t) as shown in FIG. 4 (S1, S2, S3).

H _(m) ^(P)(r−r _(c), θ_(c) , t)=H _(m)(r−r _(c), θ_(c) , t)−(H _(m)(r−r_(c), θ_(c) , t)·e _(n)(r))e _(n)(r)  (1)

[0056] This component does not contain the noise magnetic field for thereason given below. Since

H _(m) ^(P)(r−r _(c), θ_(c) , t)=H _(s)(r−r _(c), θ_(c) , t)+H _(n)(r,t)=H _(s)(r−r _(c), θ_(c) , t)+|H _(n)(r, t)|e _(n)(r)  (2)

it follows that

H _(m) ^(P)(r−r _(c), θ_(c) , t)=H _(s)(r−r _(c), θ_(c) , t)−(H _(s)(r−r_(c), θ_(c) , t)·e _(n)(r))e _(n)(r)  (3)

[0057] from which it can be seen that the projective component vectorH_(m) ^(P)(r−r_(c), θ_(c), t) does not contain the component of thenoise magnetic field vector H_(n)(r, t).

[0058] However, the projective component vector H_(m) ^(P)(r−r_(c),θ_(c), t) has lost information of one axis by the projection on a planevertical to the direction of the vector e_(n)(r). That is, since thesame projective components are obtained irrespective of the magnitude ofa component parallel to the vector e_(n)(r), two independent componentsare obtained.

[0059] Although any method can be used to obtain the two independentcomponents; it is possible to use such a method as described below.

[0060] That one of coordinate axes of a measurement coordinate systemC_(M) (which will be described later on), which is not parallel to thedirection e_(n)(r) of the noise magnetic field vector H_(n)(r, t), ischosen. Let a unit vector in the direction of the chosen coordinate axisby identified as a vector e_(m). A vector product,e_(p,1)=e_(m)×e_(n)(r), of the unit vector and the direction e_(n)(r) isperpendicular to the direction of the vector e_(n)(r), and hence it iscontained in the plane of projection and is perpendicular to thecoordinate axis e_(m). Let the magnitude of a vector obtained byprojecting the projective component vector H_(m) ^(P)(r−r_(c), θ_(c), t)in the direction of the vector e_(p,1), including the direction of thevector, be represented (S4) by a value of H_(m,1) ^(P)(r−r_(c), θ_(c),t). That is,

H _(m,1) ^(P)(r−r _(c), θ_(c) , t)=H _(m) ^(P)(r−r _(c), θ_(c) , t)·e_(p,1)  (4)

e _(p,1) =e _(m) ×e _(n)(r)  (5)

[0061] The next step is to calculate a vector e_(p,2) perpendicular tothe directions of the vectors e_(p,1) and e_(n)(r). The direction of thevector e_(p,2) is also perpendicular to the direction of the vectore_(n)(r), and hence it is contained in the plane of projection and isperpendicular to the direction of the vector e_(p,1) as well. Lettingthe projection of the projective component vector H_(m) ^(P)(r−r_(c),θ_(c), t) in this direction be represented by H_(m,2) ^(P)(r−r_(c),θ_(c), t), values H_(m,1) ^(P)(r−r_(c), θ_(c), t)e_(p,1) and H_(m,2)^(P)(r−r_(c), θ_(c), t)e_(p,2) are two independent vectors into whichthe projective component vector H_(m) ^(P)(r−r_(c), θ_(c), t) isseparated. Here,

H _(m,2) ^(P)(r−r _(c), θ_(c) , t)=H _(m) ^(P)(r−r _(c), θ_(c) , t)·e_(p,2)  (6)

e _(p,2) =e _(p,1) ×e _(n)(r)  (7)

[0062] Then, by setting the position vector r_(c) andangle-of-orientation θ_(c) of the magnetic field source so that atheoretically calculated magnetic field, H_(e)(r−r_(c), θ_(c), t)generated by the magnetic field source of the position vector rsubstantially matches with a projective component H_(e) ^(P)(r−r_(c),θ_(c), t) on the same plane as that of the measured magnetic field, itis possible to detect the position and orientation of the magnetic fieldsource.

[0063] The above description has been given of a case where the numberof noise magnetic fields is virtually one, but when the number of noisemagnetic fields is two, letting the direction of two noise magneticfields H_(n,j)(r, t), where j=1, 2, be represented by vectors e_(n1)(r)and e_(n2)(r), use is made of the projection of the measured magneticfield on a direction vector e_(N)(r)=e_(n1)(r)×e_(n2)(r) in thecoordinate system of FIG. 3 as depicted in FIG. 5. That is,

H _(m) ^(P)(r−r _(c), θ_(c) , t)=H _(m)(r−r _(c), θ_(c) , t)−(H _(m)(r−r_(c), θ_(c) , t)·e _(N)(r))e _(N)(r)  (8)

[0064] is calculated (S11, S12, S13). In the above

e _(N)(r)=e _(n1)(r)×e _(n2)(r)  (9)

[0065] where the symbol “×” indicates a vector product. In thisinstance, an independent component in the projective component is one,that is, oily the magnitude of the vector.

[0066] Now, let the coordinates of the magnetic field source berepresented by a vector r_(c)(x, y, z) and its angle of orientation by avector θ_(c)(θ_(x), θ_(y), θ_(z)). In the following description, θ_(x),θ_(y) and θ_(z) will be referred to as an angle of rotation, a tiltangle and an azimuth, respectively. When the signal magnetic field isaxially symmetric, the axis of symmetry is regarded as the x-axis, andthe angle of orientation is set to a vector θ_(c)(θ_(y), θ_(z)).

[0067] Further, according to the present invention, it is possible tocalculate the magnitude H_(m)(r−r_(c), θ_(c)) of each component of theoriginal signal magnetic field vector H_(m)(r−r_(c), θ_(c), t) bysynchronous detection of the measured magnetic field vectorH_(m)(r−r_(c), θ_(c), t) through the use of a proper one component inEq. (1) or (6) that is a projective component.

H _(s)(r−r _(c), θ_(c))=

H _(m)(r−r _(c), θ_(c) , t)H _(m) ^(P)(r−r _(c), θ_(c) , t)

_(t)  (10)

[0068] In the above, H_(m) ^(P)(r−r_(c), θ_(c), t) is a proper componentof the projective component given in Eq. (1) or (6).

[0069]FIG. 4 shows the case where the number of noise magnetic fieldsources is essentially one. The processing of FIG. 4 is repeated at eachmeasuring point. hi the case of essentially two noise magnetic fields,too, the processing shown in FIG. 5 is repeated at each measuring pointas is the case with FIG. 4.

[0070] The magnitude H_(m)(r−r_(c), θ_(c)) of the original signalmagnetic field H_(m)(r−r_(c), θ_(c), t) can be obtained by calculatingEq. (10) after calculating the projective component at each measuringpoint. Concretely, the processing depicted in FIG. 6 or 7 is carried out[(S11, S12, S14, S15, S16) or (S11, S12, S14 a, S16)].

[0071] How to Calculate the Position and Angle of Orientation

[0072] (1) Definitions of the Coordinate System and the Angle ofOrientation:

[0073] A definition will be given first of the coordinate systemnecessary for the description of the invention.

[0074] A coordinate system is set which is fixed to the earth with thez-axis in a vertical direction (upward), which system will hereinafterbe referred to as a measuring coordinate system vector C_(M). The x-andy-axes are properly set so that they form a right-hand system. Forexample, they are set in parallel to the direction in which the side ofa measuring frame is projected on a horizontal plane.

[0075] This has for its object to calculate the coordinate vectorr_(e)(x, y, z) and angle-of orientation vector θ_(c)(θ_(x), θ_(y),θ_(z)) of the magnetic field source in the coordinate system.

[0076] On the other hand, as the coordinate system vector C_(c) of themagnetic field source, a coordinate system with the axial direction ofthe magnetic field source as the x axis is set so that the y-and z-axesare horizontal and vertical (upward), respectively, when the magneticfield source is placed horizontally.

[0077] The angle-of-orientation vector θ_(c) of the magnetic fieldsource is defined as the angle of rotation between the measuringcoordinate system vector C_(M) and tie coordinate system vector C_(c) asdescribed below. In the first place, a coordinate system C_(c0) parallelto the measuring coordinate system vector C_(M) is turned by an azimuthangle θ0 _(z) about the z-axis (in either one of the coordinate system).This coordinate system will be referred to as a coordinate system vectorC_(c1). Next, the coordinate system vector C_(c1) is turned by a tiltangle θ_(y) about the y-axis of the coordinate system vector C_(c1)itself This coordinate system will be referred to as a coordinate systemvector C_(c2). Further, the coordinate system vector C_(c2) is turned byan angle of rotation Oz about the x-axis of the coordinate system vectorC_(c2) itself The angle-of-orientation vector θ_(c) is determined sothat the resulting coordinate system becomes the coordinate systemvector C_(c).

[0078] (2) Explanation of Independent Measurands and Unknowns:

[0079] When the number of noise magnetic fields is essentially one, themeasurement of the magnetic field at one place will provide twoindependent measurands. When the number of noise magnetic fields isessentially two, the measurement of the magnetic field at one place willprovide one independent measurand. Further, in case of obtainingcomponents of the original signal magnetic field by synchronousdetection, the measurement of the magnetic field at one place willprovide three independent measurands. On the other hand, threecoordinate components of the coordinate vector r_(c)(x, y, z) of themagnetic field source are unknowns. The azimuth angle θ_(z) is notobtainable without a different criterion such as the direction of theearth magnetism, and hence it is also an unknown unless the digging headis provided with a direction sensor. When the digging head is made of amagnetic material, or when a buried steel pipe or similar magnetic bodylies near the digging head, an accurate direction cannot be-obtainedeven if the direction sensor is provided; hence, the azimuth angle θ_(z)is an unknown in many cases. The tilt angle θ_(y) can easily be detectedby a tilt angle sensor that detects the vertical direction, and hence itis known in many cases. The same is true of the angle of rotation θ_(x).In particular, when the signal magnetic field is- axially symmetric, ifthe axis of symmetry is regarded as the x-axis, the angle of rotationθ_(x) becomes meaningless and hence can be ignored.

[0080] At any rate, measured magnetic fields need only to be obtained atdifferent positions so that independent measurands larger in number thanunknowns.

[0081] Arrangement of the Measuring System

[0082] For example, as shown in FIG. 1, magnetic fields are measuredusing a required number of three-axis magnetic sensors disposed on theground so that their relative positions are known. Since the directionof the noise magnetic field changes for each position of measurement, itis necessary to perform for each position the step (S21) for detectingthe position of the noise magnetic field and the step (S22) forcalculating the projective component of the measured magnetic field asshown in FIG. 8 that is a flowchart of the procedure for positiondetermination by the present invention. in case of calculating thecomponent of the original signal magnetic field by synchronousdetection, the processing therefor (in a specified step) needs to becarried out for each position.

[0083] Flow of Measurement Processing

[0084] A detailed description will be given of the detection (S21) ofthe direction of the noise magnetic field, the calculation (S23) of theposition of the signal magnetic field source through the use of theprojective component and the calculation of the position f of the signalmagnetic field through the use of the signal magnetic field component.

EMBODIMENTS

[0085] Embodiment in the Case of Virtually One Noise Magnetic Field:

[0086] in case of using the projective component, when the number ofunknowns is N_(U)(≧1) and the number of noise magnetic fields isvirtually one, the projective component vector H_(m) ^(P)(r−r_(c),θ_(c), t) expressed by Eq. (1) is calculated from magnetic vectorsH_(m)(r−r_(c), θ_(c), t) measured at N_(U)/2 or more differentpositions, and the position vector r_(c) and the angle-of-orientationvector θ_(c) are determined (S31) as depicted in FIG. 9 so that aprojective component vector at each magnetic field sensing point isessentially equal to the projective component vector H_(e) ^(P)(r−r_(c),θ_(c), t) of a theoretically calculated magnetic field of the projectivecomponent at each position of measurement, by which it is possible todetect (S32) the position and orientation of the magnetic field source.

[0087] In case of using the magnitude of the signal magnetic fieldsynchronously detected by the projective component, the magnetic fieldis measured at N^(U)/3 or more different positions. When the numberN_(U)(≧1) of unknowns is even, the number of unknowns and the number ofindependent measurands can be made equal to each other; if settingmagnetic field vector H_(m)(r−r_(c), θ_(c), t) is measured at positionsN_(m)=N_(U)/2, a N_(U) number of such equations as given below need onlyto be solved.

H _(m,q) ^(P)(r _(k) −r _(c), θ_(c) , t)

_(t) −H _(e,q) ^(P)(r _(k) −r _(c), θ_(c))=0, k=1, . . . , N _(m) ; q=1,2.   (11)

[0088] where q=1, 2 and represents two directions parallel to the planeof projection but parallel to each other (S33). Accordingly, H_(m,q)^(P)(r−r_(c), θ_(c), t) and H_(e,q) ^(P)(_(r−r) _(c), θ_(c), t), whereq=1, 2, are the magnitudes of q-direction components of the measuredmagnetic field vector H_(m)(r−r_(c), θ_(c), t) and the theoreticalcalculated magnetic field vector H_(e)(r−r_(c), θ_(c), t), respectively.Let it be assumed that the vector θ_(c) represents any one of θ_(x),θ_(y), θ_(z)(θ_(y), θ_(z)), (θ_(z), θ_(x)), (θ_(x), θ_(y)), (θ_(x),θ_(y), θ_(z)) and Φ and that the vector r_(c) represents any one of x,y, z, (y, z), (z, x), (x, y), (x, y, z) and Φ, where Φ represents anempty set.

[0089] For example, when unknowns are the position vector r_(c)(x, y, z)and azimuth angle θ_(z) of the magnetic field source, the magnetic fieldis to be measured at two different positions and four equations such asgiven below are solved, by which. it is possible to obtain (S34) theposition vector r_(c)(x, y, z) and azimuth angle θ_(z) of the magneticfield source.

H _(m,q) ^(P)(r _(k) −r _(c), θ_(z) , t)

_(t) −H _(e,q) ^(P)(r _(k) − r _(c), θ_(z))=0, k=1, 2; q=1, 2.  (12)

[0090] In the above, <.>_(t) represents a time average.

[0091] As depicted in FIG. 10, when the magnetic field is measured atN_(m)(>N_(U)/2) different places more than N_(U)/2 in excess of thenumber N_(U) of unknowns, since a larger number of independentmeasurands than the number of unknowns can be obtained (S41, S42, S43),the position r_(c)(e, y, z) and the angle of orientation θ_(z) arecalculated which provide $\begin{matrix}{\min\limits_{r_{c},\theta_{c}}{\left\{ {\sum\limits_{k = 1}^{N_{m}}{\sum\limits_{q = 1}^{2}{w_{k,q}{{{\langle{{H_{m,q}^{P}\left( {{r_{k} - r_{c}},\theta_{c},t} \right)}}\rangle}_{t} - {H_{e,q}^{P}\left( {{r_{k} - r_{c}},\theta_{c}} \right)}}}}}} \right\}.}} & (13)\end{matrix}$

[0092] where <.>_(t) represents the time average and$\min\limits_{r_{c},\theta_{z}}\left\{ . \right\}$

[0093] means that vectors r_(c) and θ_(c) are changed to obtain vectorsr_(c) and θ_(c) that minimize the contents in {.}. Further, a symbolw_(k,q) indicates weighting. The Eq. (13) can be replaced with thefollowing equations (S44). $\begin{matrix}{\min\limits_{r_{c},\theta_{c}}{\left\{ {\sum\limits_{k = 1}^{N_{m}}{\sum\limits_{q = 1}^{2}{w_{k,q}{{\sqrt{{\langle{{H_{m,q}^{P}\left( {{r_{k} - r_{c}},\theta_{c},t} \right)}}^{2}\rangle}_{t}} - {H_{e,q}^{P}\left( {{r_{k} - r_{c}},\theta_{c}} \right)}}}}}} \right\}.}} & (14) \\{\min\limits_{r_{c},\theta_{z}}{\left\{ {\sum\limits_{k = 1}^{N_{m}}{\sum\limits_{q = 1}^{2}{w_{k,q}{{{\langle{{H_{m,q}^{P}\left( {{r_{k} - r_{c}},\theta_{c},t} \right)}}\rangle}_{t} - {H_{e,q}^{P}\left( {{r_{k} - r_{c}},\theta_{z}} \right)}}}^{2}}}} \right\}.}} & (15) \\{\min\limits_{r_{c},\theta_{z}}{\left\{ {\sum\limits_{k = 1}^{N_{m}}{\sum\limits_{q = 1}^{2}{w_{k,q}{{\sqrt{{\langle{{H_{m,q}^{P}\left( {{r_{k} - r_{c}},\theta_{c},t} \right)}}^{2}\rangle}_{t}} - {H_{e,q}^{P}\left( {{r_{k} - r_{c}},\theta_{z}} \right)}}}^{2}}}} \right\}.}} & (16)\end{matrix}$

[0094] Assume that vectors r_(c) and θ_(c) in Eqs. (13), (14), (15) and(16) have the same meaning as in the case of Eq. (11).

[0095] In the above description it does not matter whether the measuredmagnetic field vector H_(m)(r−r_(c), θ_(c), t) is a signal having passedthrough a band pass filter that permits the passage therethrough of onlycomponents close to the frequency of the signal magnetic field or awide-band signal that is inhibited from the passage through the baldpass filter, but the use of the signal having passed through the bandpass filter increases the possibility of determining the position of themagnetic :field with high reliability.

[0096] Embodiment in the Case of Essentially Two Noise Magnetic Fields

[0097] When the number of unknowns is N_(U)(>1) and the number of noisemagnetic fields is virtually two, the projective component vector H_(m)^(P)(r−r_(c), θ_(c), t) expressed by Eq. (4) is calculated from magneticvectors H_(m)(r−r_(c), θ_(c), t) measured at N_(U)/2 or more differentpositions, and the position vector r_(c) and the angle-of-orientationvector θ_(c) are determined (S51, S52) as depicted in FIG. 11 so thatthe above-mentioned projective component vector obtained at eachposition of measurement essentially matches with the projectivecomponent vector H_(e) ^(P)(r−r_(c), θ_(c), t) of a theoreticallycalculated magnetic field at each position of measurement, by which itis possible to detect (S53) the position and orientation of the magneticfield source.

[0098] In this case, the number N_(U)(>1) of unknowns and the number ofindependent measurands can be made to be equal to each other withoutfail; the magnetic field vector H_(m)(r−r_(c), θ_(c), t) is measured atdifferent positions of the same number as that N_(U) number of unknowns,and N_(U) number of such equations given below need only to be solved.

H _(m) ^(P)(r _(k) −r _(c), θ_(c) , t)

_(t) −H _(c) ^(P)(r _(k) −r _(c), θ_(c))=0, k=1, . . . , N _(U)  (17)

[0099] In this case, symbols H_(m) ^(P)(r−r_(c), θ_(c), t) and H_(e)^(P)(r−r_(c), θ_(c), t) are the respective magnitudes of the projectivecomponent vector H_(m)(r−r_(c), θ_(c), t) and the vector H_(e)^(P)(r−r_(c), θ_(c), t) of the measured magnetic field vectorH_(m)(r−r_(c), θ_(c), t) and the theoretical calculated magnetic fieldvector H_(e)(r−r_(c), θ_(c), t). Let it be assumed that the vector θ_(c)represents any one of θ_(x), θ_(y), θ_(z), (θ_(y), θ_(z)), (θ_(z),θ_(x)), (θ_(x), θ_(y)), (θ_(x), θ_(y), θ_(z)) and Φ and that the vectorr, represents any one of x, y, z, (y, z), (z, x), (x, y), (x, y, z) andΦ, where Φ represents an empty set.

[0100] For example, when unknowns are the position vector r_(c)(x, y,z), azimuth angle θ_(z) and tilt angle θ_(y) of the magnetic fieldsource, the magnetic field is to be measured at five different positionsand four such equations given below are solved, by which it is possibleto obtain the position vector r_(c)(x, y, z), azimuth angle θ_(z) andtilt angle θ_(y) of the magnetic field source.

H _(m) ^(P)(r _(k) −r _(c), θ_(c)

, t)

_(t) −H _(e) ^(P)(r _(k) −r _(c), θ_(c))=0, k=1, . . . ,5  (18)

[0101] In the above, <.>_(t) represents a time average. And the vectorθ_(c)=θ_(c)(θ_(y), θ_(z)).

[0102] As depicted in FIG. 12, when the magnetic field is measured atN_(m)(>N_(U)) different places more than N_(U) in excess of the numberN_(U)of unknowns, since a larger number of independent measurands thanthe number of unknowns can be obtained (S61, S62), the position r_(c)(e,y, z) and the angle of orientation θ_(z) are calculated which provide$\begin{matrix}{\min\limits_{r_{c},\theta_{c}}{\left\{ {\sum\limits_{k = 1}^{N_{m}}{w_{k}{{{\langle{{H_{m}^{P}\left( {{r_{k} - r_{c}},\theta_{c},t} \right)}}\rangle}_{t} - {H_{e}^{P}\left( {{r_{k} - r_{c}},\theta_{c}} \right)}}}}} \right\}.}} & (19)\end{matrix}$

[0103] where <.>_(t) represents the time average and$\min\limits_{r_{c},\theta_{z}}\left\{ . \right\}$

[0104] means that vectors r_(c) and θ_(c) are changed to obtain r_(c)and θ_(c) that minimize the contents in {.} Further, a symbol w_(k,q)indicates weighting. The Eq. (19) can be replaced with tile followingequations (S63). $\begin{matrix}{\min\limits_{r_{c},\theta_{c}}{\left\{ {\sum\limits_{k = 1}^{N_{m}}{w_{k}{{\sqrt{{\langle{{H_{m}^{P}\left( {{r_{k} - r_{c}},\theta_{c},t} \right)}}^{2}\rangle}_{t}} - {H_{e}^{P}\left( {{r_{k} - r_{c}},\theta_{c}} \right)}}}}} \right\}.}} & (20) \\{\min\limits_{r_{c},\theta_{z}}{\left\{ {\sum\limits_{k = 1}^{N_{m}}{w_{k}{{{\langle{{H_{m}^{P}\left( {{r_{k} - r_{c}},\theta_{c},t} \right)}}\rangle}_{t} - {H_{e}^{P}\left( {{r_{k} - r_{c}},\theta_{z}} \right)}}}^{2}}} \right\}.}} & (21) \\{\min\limits_{r_{c},\theta_{z}}{\left\{ {\sum\limits_{k = 1}^{N_{m}}{w_{k}{{\sqrt{{\langle{{H_{m}^{P}\left( {{r_{k} - r_{c}},\theta_{c},t} \right)}}^{2}\rangle}_{t}} - {H_{e}^{P}\left( {{r_{k} - r_{c}},\theta_{c}} \right)}}}^{2}}} \right\}.}} & (22)\end{matrix}$

[0105] Assume that r_(c) and θ_(c) in Eqs. (19), (20), (21 ) and (22)have the same meaning as in the case of Eq. (16).

[0106] In the above description, it does not matter whether the measuredmagnetic field vector H_(m)(r−r_(c), θ_(c), t) is a signal having passedthrough a band pass filter that permits the passage therethrough of onlycomponents close to the frequency of the signal magnetic field, or awide-band signal that is inhibited from the passage through the bandpass filter, but the use of the signal having passed through the bandpass filter increases the possibility of determining the position of themagnetic field with high reliability.

[0107] Further, in case of using the signal magnetic field componentobtained by synchronous detection, the direction of the noise magneticfield is determined and is used to obtain the projective magnetic field;and the subsequent processing is common to the cases of one and twonoise magnetic fields. The projective component vectors H_(m)^(P)(r−r_(c), θ_(c), t) at respective places are calculated frommagnetic field vectors H_(m)(r−r_(c), θ_(c), t) measured at N_(U)/3 ormore different places, and a proper one of the calculated vectors isused as a reference signal to perform synchronous detection of themeasured magnetic field vectors H_(m)(r−r_(c), θ_(c), t), therebyobtaining the magnitude H_(s)(r−r_(c), θ_(c)) of the original signalmagnetic field component. By determining the position vector r_(c) andthe angle-of-orientation vector θ_(c) of the magnetic field source sothat the magnitude of the original signal magnetic field component andthe magnitude H_(c)(r−r_(c), θ_(c)) of the theoretical signal componentare equal to each other, it is possible to detect the position andorientation of the magnetic field source.

[0108] When the number N_(U)(>2) of unknowns is a multiple of 3, thenumber of unknowns and the number of independent measurands can be madeto be equal to each other; if the magnetic field vector H_(m)(r−r_(c),θ_(c), t) is measured at positions N_(m)=N_(m)/N_(U)/3, N_(U) number ofsuch equations as given below need only to be solved.

H _(s)(r _(k) −r _(c), θ_(c))=0, k=1, . . . , N _(m)  (23)

[0109]FIG. 13 shows the flow of processing (S61, S62, S65). Here,H_(s)(r−r_(c), θ_(c)) and H_(c)(r−r_(c), θ_(c), t) are the signalmagnetic field calculated from the measured magnetic field vectorsH_(m)(r−r_(c), θ_(c), t) and the magnitude of the theoretical calculatedmagnetic field vector, respectively. The magnitude H_(s)(r−r_(c), θ_(c))of the signal magnetic field vector is an averaged quantity as alreadyexplained. Let it be assumed that the vector θ_(c) represents any one ofθ_(x), θ_(y), θ_(z), (θ_(y), θ_(z)), (θ_(z), θ_(x)), (θ_(x), θ_(y)),(θ_(x), θ_(y), θ_(z)) and Φ and that the vector r_(c) represents any oneof x, y, z, (y, z), (z, x), (x, y), (x, y, z) and Φ, where Φ representsan empty set.

[0110] For example, when an unknown is the position vector r_(c)(x, y,z) of the magnetic field source, the magnetic field is to be measured atone place and three such equations as given below are solved, by whichit is possible to obtain the position vector r_(c)(x, y, z) and azimuthangle θ_(z) of the magnetic field source.

H _(s)(r−r _(c))−H _(c)(r−r _(c))=0.  (24)

[0111] The vector r is the vector of the position of measurement.

[0112] When the magnetic field is measured at N_(m)(>N_(U)/2) differentplaces more than N_(U) in excess of the number N_(U) of unknowns, sincea larger number of independent measurands than the number of unknownscan be obtained, the position r_(c)(e, y, z) and the angle oforientation θ_(z) are calculated which provide $\begin{matrix}{\min\limits_{r_{c},\theta_{c}}{\left\{ {\sum\limits_{k = 1}^{N_{m}}{w_{k}{{{H_{s}\left( {{r_{k} - r_{c}},\theta_{c}} \right)} - {H_{c}\left( {{r_{k} - r_{c}},\theta_{c}} \right)}}}}} \right\}.}} & (25)\end{matrix}$

[0113] where $\min\limits_{r_{c},\theta_{z}}\left\{ . \right\}$

[0114] means that vectors r_(c) and θ_(c) are changed to obtain vectorsr_(c) and θ_(c) that minimize the contents in {.}. Further, a symbolw_(k,q) indicates weighting. The Eq. (25) can be replaced with thefollowing equations. $\begin{matrix}{\min\limits_{r_{c},\theta_{c}}{\left\{ {{\sum\limits_{k = 1}^{N_{m}}w_{k}},\left( {{{H_{s}\left( {{r_{k} - r_{c}},\theta_{c}} \right)}} - {{H_{c}\left( {{r_{k} - r_{c}},\theta_{c}} \right)}}} \right)^{2}} \right\}.}} & (26) \\{\min\limits_{r_{c},\theta_{z}}{\left\{ {\sum\limits_{k = 1}^{N_{m}}{w_{k}{{{H_{s}\left( {{r_{k} - r_{c}},\theta_{c}} \right)} - {H_{c}\left( {{r_{k} - r_{c}},\theta_{c}} \right)}}}^{2}}} \right\}.}} & (27)\end{matrix}$

[0115]FIG. 14 shows the flow of processing (S61, S64, S66).

[0116] A description will be given below of how to determine thedirection of the noise magnetic field in the two embodiments describedabove.

[0117] How to Determine the Direction of the Noise Magnetic Field in theCase of Virtually One Noise Magnetic Field

[0118] First Method

[0119] The first method for determining the direction of the noisemagnetic field is a method where, in case of no signal magnetic field, anoise magnetic field is measured through the use of the same measuringsystem as that for measuring the signal magnetic field. This situationis such as shown in FIG. 15 in which the detection of the diggingposition is disturbed by a noise magnetic field source lying in thevicinity of the digging route. Another case is that where the signalmagnetic field source is equipped with a function of receiving a commandsent, for example, from the ground by some means and responsive to thecommand to stop the generation of the signal magnetic field.

[0120] In this instance, as depicted in FIG. 16, letting the measuredmagnetic field be represented by a vector H_(m)(r−r_(c), θ_(c), t),since this is essentially a noise magnetic field vector _(n)(r, t) asshown at a step (S71), an average value of its absolute values can beused (S72) to calculate a direction vector, e_(n)(r)=e_(n),_(x)(r),e_(n),_(y)(r), e_(n),_(z)(r)), of the noise magnetic field as follows:$\begin{matrix}{{{e_{n,\alpha}(r)} = \frac{{\langle{{H_{m,\alpha}\left( {{r - r_{c}},\theta_{c},t} \right)}}\rangle}_{t}}{\sqrt{\sum\limits_{{\alpha = x},y,z}{\langle{{H_{m,\alpha}\left( {{r - r_{c}},\theta_{c},t} \right)}}\rangle}^{2}}}},{\alpha = x},y,{z.}} & (28)\end{matrix}$

[0121] Alternatively, a root-mean-square value of the above absolutevalues can be used to determine the direction of the noise magneticfield by $\begin{matrix}{{{e_{n,\alpha}(r)} = \frac{\sqrt{{\langle\left( {H_{m,\alpha}\left( {{r_{k} - r_{c}},\theta_{c},t} \right)} \right)^{2}\rangle}_{t}}}{\sqrt{\sum\limits_{{\alpha = x},y,z}{\langle\left( {H_{m,\alpha}\left( {{r_{k} - r_{c}},\theta_{c},t} \right)} \right)^{2}\rangle}_{t}}}},{\alpha = x},y,{z.}} & (29)\end{matrix}$

[0122] In this case, a symbol H_(m,α)(r−r_(c), θ_(c), t) is an cccomponent of the measured magnetic field (the noise magnetic field), andα is any one of x, y and z.

[0123] In the above description it does not matter whether the measuredmagnetic field vector H_(m)(r−r_(c), θ_(c), t) is a signal having passedthrough a band pass filter that permits the passage therethrough of onlycomponents close to the frequency of the signal magnetic field or awide-band signal that is inhibited from the passage through the bandpass filter, but the use of the signal having passed through the bandpass filter increases the possibility of determining the position of themagnetic field with high reliability.

[0124] Second Method

[0125] Step 1

[0126] As shown in FIG. 17, at first , the frequency spectrum H_(m)(ω)of the measured magnetic field vector H_(m)(r−r_(c), θ_(c), t) iscalculated (S81, S82, S83) lily the following equation.

H _(m)(ω)=F(H _(m)(r _(k) −r _(c), θ_(c) ,t))  (30)

[0127] In this case, a symbol F(.) represents a Fourier transform; thethree components x, y and z of the measured magnetic field vectorH_(m)(r−r_(c), θ_(c), t) are each Fourier transformed. In practice, theabove-mentioned frequency spectrum can be calculated by FFT (fastFourier transform) or the like of sampled values of the measuredmagnetic field vector H_(m)(r−r_(c), θ_(c), t).

[0128] Step 2

[0129] Next, an angular frequency ω_(i), where i=1, 2, . . . , N_(s), ofa large-amplitude component, such as a line spectrum, is selected (S84)from the absolute value |H_(m)(ω)| of the frequency spectrum. For thecomponent of each angular frequency ω_(i), where i=1, 2, . . . , N_(ns),a candidate unit vector e_(n)(r, ω_(i)), where i=1, 2, . . . , N_(ns),of the direction of the noise magnetic field, is calculated (S85) by themethod (1) or (2) described below.

[0130] (1) The absolute values of the Fourier-transformed x, y, and zcomponents of the angular frequency concerned are used to calculate thecandidate unit vector e_(n)(r, ω_(i)), where i=1, 2, . . . , N_(ns), ofthe direction of the noise magnetic field, by the following procedures:$\begin{matrix}{{{e_{n}\left( {r,\omega_{i}} \right)} = \frac{\left( {{{H_{m,x}\left( \omega_{i} \right)}}{{H_{m,x}\left( \omega_{i} \right)}}{{H_{m,x}\left( \omega_{i} \right)}}} \right)}{\sqrt{\sum\limits_{{\alpha = x},y,z}{{H_{m,\alpha}\left( \omega_{i} \right)}}^{2}}}},{i = 1},\quad \ldots \quad,{N_{n\quad s}.}} & (31)\end{matrix}$

[0131] where H_(m,α)(ω_(i)), where α=x, y, z and i=1, 2, . . . , N_(ns),is a ω_(i) component by the Fourier transform of the a component of themeasured magnetic field.

[0132] (2) A narrow-band filter is formed whose pass band uses, as thecenter frequency, the angular frequency ω_(i), where i=1, 2, . . . ,N_(ns), and the same method as by Eq. (21) or (22) is used to calculatethe candidate unit vector e_(n)(r, ω_(i)), where i=1, 2, . . . , N_(ns).That is, the candidate unit vector e_(n)(r, ω_(i))=(e_(n,x)(r),e_(n,y)(r), e_(n,z)(r)), where i=1, 2, . . . , N_(ns),is calculated by$\begin{matrix}{{{e_{n,\alpha}\left( {r,\omega_{i}} \right)} = \frac{{\langle{{H_{m,\alpha}\left( {{r - r_{c}},\theta_{c},\omega_{i},t} \right)}}\rangle}_{t}}{\sqrt{\sum\limits_{{\alpha = x},y,z}{\langle{{H_{m,\alpha}\left( {{r - r_{c}},\theta_{c},\omega_{i},t} \right)}}\rangle}^{2}}}},{\alpha = x},y,{z;{i = 1}},\quad \ldots \quad,{N_{n\quad s}.}} & (32)\end{matrix}$

[0133] or by $\begin{matrix}{{{e_{n,\alpha}\left( {r,\omega_{i}} \right)} = \frac{\sqrt{{\langle\left( {H_{m,x}\left( {{r_{k} - r_{c}},\theta_{c},\omega_{i},t} \right)} \right)^{2}\rangle}_{t}}}{\sqrt{\sum\limits_{{\alpha = x},y,z}{\langle\left( {H_{m,\alpha}\left( {{r_{k} - r_{c}},\theta_{c},\omega_{i},t} \right)} \right)^{2}\rangle}_{t}}}},{\alpha = x},y,{z;{i = 1}},\quad \ldots \quad,{N_{n\quad s}.}} & (33)\end{matrix}$

[0134] Step 3

[0135] The candidate unit vector e_(n)(r, ω_(i))=(e_(n,x)(r),e_(n,y)(r), e_(n,z)(r)), where i=1, 2, . . . , N_(ns), is considered asthe direction vector e_(n)(r) of the noise magnetic field, and for eachangular frequency ω_(i), where i=1, 2, . . . , N_(ns), the same methodas by Eq. (1) is used to calculate a projective component vector H_(m)^(P)(r−r_(c), θ_(c), C , t).

H _(m) ^(P)(r−r _(c), θ_(c), ω_(i) , t)=H _(m)(r−r _(c), θ_(c) ,t)−(H_(m)(r−r _(c), θ_(c) , t)·e _(n)(r, ω _(i)))e _(n)(r, ω _(i)), i=1,. . . , N _(ns).  (34)

[0136] The reason for which lithe angular frequency ω_(i) is containedas a variable of the projective component is to explicitly point outthat the projective component is dependent on the angular frequencyω_(i), where i=1, 2, . . . , N_(ns). A roper time interval T_(test),which consists of N_(test) durations T_(t,k), where k=1, 2, . . . ,N_(test), each having a short time length Δt, is chosen, and thevariation of the projective component vector H_(m) ^(P)(r−r_(c), θ_(c),ω_(i), t) for each duration T_(t,k), where k=1, 2, . . . , N_(test), isevaluated (S86). Assume, here, that each duration T_(t,k), where k=1, 2,. . . , N_(test) does not overlap other durations. Concretely, avariance of N_(test) statistics v_(eval,k)(ω_(i)) of the N_(test), wherek=1, . . . , N_(test), which are calculated by any one of the methodsdescribed below, is calculated.

[0137] (1) One or both of the means of absolute values of two orthogonalcomponents by

ν_(eval, k)

|H _(m,q) ^(P)(r−r _(c), θ_(c), ω_(i) , t)|

_(Tt,k) , q=1, 2; k=1, . . . , N _(test) ; i=1, . . . , N _(ns).  (35)

[0138] where

.

_(Tt,k) represents the mean value in the duration T_(t,k) and v_(eval,k)is a statistic calculated for the duration T_(t,k).

[0139] (2) Mean of Absolute Values

ν_(eval,k)(ω_(i))=

|H _(m) ^(P)(r−r _(c), θ_(c), ω_(i) , t)|

_(T) _(t,k) , k=1, . . . , N _(test) ; i=1, . . . , N _(ns).  (36)

[0140] (3) One or both of the means of squares of two orthogonalcomponents by

ν_(eval,k)(ω_(i))=

(H _(m,q) ^(P)(r−r _(c), θ_(c), ω_(i) , t))²

_(T) _(t,k) , q=1, 2; k=1, . . . , N_(test) ; i=1, . . . , N_(ns).  (37)

[0141] (4) One or both of square roots of the means of squares of twoorthogonal components by

ν_(eval,k)(ω_(i))={square root}{square root over (

(H _(m,q) ^(P)(r−r _(c), θ_(c), ω_(i) , t)) ²

_(T) _(t,k) )}, q=1, 2; k=1, . . . , N _(test) ; i=1, . . . , N _(ns).  (38)

[0142] For the statistics νeval,k, where k=1, . . . , N_(test),calculated by these equations, the following equation $\begin{matrix}{{{{var}\left( \omega_{i} \right)} = \frac{\sqrt{{mean}_{k}\left( \left( {{v_{{eval},k}\left( \omega_{i} \right)} - {{mean}_{k}\left( {v_{{eval},k}\left( \omega_{i} \right)} \right)}} \right)^{2} \right)}}{{mean}_{k}\left( {v_{{eval},k}\left( \omega_{i} \right)} \right)}},{i = 1},\quad \ldots \quad,{N_{n\quad s}.}} & (39)\end{matrix}$

[0143] is calculated to obtain (S86) a value of ω_(i,min) that is theangular frequency ω_(i) which minimizes var(ω_(i)). In the above,mean_(k)(.) indicates averaging for the suffix k, that is,$\begin{matrix}{{{mean}_{k}\left( . \right)} = {\frac{\sum\limits_{k = 1}^{N_{test}}\quad \left( . \right)}{N_{test}}.}} & (40)\end{matrix}$

[0144] The magnetic field of the angular frequency ω_(i,min) derivesfrom the noise magnetic field, and the direction of the noise magneticfield becomes a vector e_(n)(r, ω_(i,min)).

[0145] Incidentally, the angular frequency ω_(i,min), which minimizesvar(ω_(i)), needs only to be measured at one place and need not beobtained at every place where to measure the magnetic field.

[0146] With this method, it is also possible to calculate a fluctuationin the direction of a vector H_(m) ^(p)(r−r_(c), θ_(c), ω_(i), t) aswell as an amplitude fluctuation given by Eq. (39) and to select theangular frequency ω_(i,min) at which the direction fluctuation becomesminimum or smaller than a predetermined value.

[0147] Incidentally, in the above description, the measured magneticfield vector H_(m)(r−r_(c), θ_(c), t) in Step 1 is a wide-band signal,and in Step 3 it does not matter whether the measured magnetic fieldvector H_(m)(r−r, θ_(c), t) is a signal having passed through a bandpass filter that permits the passage therethrough of only componentsclose to the frequency of the signal magnetic field or a wide-bandsignal that is inhibited from the passage through the band pass filter,but the use of the signal having passed through the band pass filterincreases the possibility of determining the position of the magneticfield with high reliability.

[0148]FIG. 18 shows how to select frequencies f₁(=ω₁/2π), f₂(=ω₂/2π), .. . , f_(n)(=ω_(n)/2π, where n=N_(ns)), at which the frequency spectrumbecomes maximum; FIG. 19 shows the flow of processing including step S91for obtaining the candidate vector; and FIGS. 20 and 21 show the flow ofprocessing including steps S101 and S102 or steps S111 and S112 forevaluating the candidate vector and for detecting the direction of thenoise magnetic field.

[0149] The frequency spectrum H_(m)(ω) need not always be used. That is,hie signal magnetic field is periodically turned OFF/ON following apredetermined procedure; the period T_(period) is divided intoequally-spaced durations; the candidate unit vector e_(n)(r, t), wherei=1, . . . , N_(ns) is used in place of the candidate unit vectore_(n)(r, ωi), where i=1, . . . , N_(ns), which is calculated by Eqs.(25), (26) and (27); and thereafter, the duration that minimized thevariance by Eq. (33) is calculated by the processing described above. Bythis, the vector e_(n)(r, t_(i)) in that duration can be adopted as thedirection of he noise magnetic field.

[0150] Third Method

[0151] In the second method, the large-amplitude angular frequencyω_(i), where i=1, 2, . . . , N_(s), is selected from the absolute value|H_(m)(ω)| of the frequency spectrum H_(m)(ω), but the vector e_(n)(r,ωi,min) call be obtained as the direction of the noise magnetic field inexactly the same manner as in the case of the second method, byselecting a proper frequency band neighboring the frequency of thesignal magnetic field, setting properly-spaced test frequencies freefrom the frequency of the signal magnetic field in the frequency bandand regarding the test frequencies as the angular frequency co; in thesecond method.

[0152] As is die case with the second method, the angular frequencyω_(i,min) at which var(ω_(i)) becomes minimum needs only to be obtained.

[0153]FIG. 22 shows how to select the frequencies f₁(=ω₁/2π),f₂(=ω₂/2π), . . . , f_(n)(=(ω_(n)/2π, where n=N_(ns)) at which thefrequency spectrum becomes maximum. The flow of the subsequentprocessing is the same as depicted in FIGS. 17, 19 and 20.

[0154] Fourth Method

[0155] The signal magnetic field is periodically stopped under controlof a predetermined procedure. For example, the signal magnetic field isperiodically stopped by a predetermined time interval. Since theintensity of the magnetic field being measured decreases while thesignal magnetic field is stopped, the OFF period of the signal magneticfield is identified by regarding the intensity-decreasing periodessentially as the predetermined OFF period, and the direction of themagnetic field measured during the OFF period is used as the directionof the noise magnetic field. The direction of the noise magnetic fieldcan be obtained using the same method as the first one. FIG. 23 showshow the amplitude of the measured magnetic field in this method varieswith time.

[0156] Fifth Method

[0157] The signal magnetic field is periodically stopped following apredetermined procedure. This is carried out as described below under(1) and (2).

[0158] (1) To stop the signal magnetic field on a rectangular-wave-wise:

[0159] The signal magnetic field is repeatedly turned ON and OFF -withthe period T_(period), for instance. $\begin{matrix}\begin{matrix}{{{s(t)} = 1},} & {t_{k} \leq t < {t_{k} + {t_{stop}.}}} \\{\quad {{= {- 1}},}} & {{t_{k} + t_{stop}} \leq t \leq {t_{k + 1}.}}\end{matrix} & (41)\end{matrix}$

[0160] and when a sequence s(t) is 1, the signal magnetic field isturned OFF, but when the sequence is −1, the signal magnetic field isturned ON. In the above,

t _(k +1) t _(k) =T _(period) , k=1, 2, 3,   (42)

[0161] (2) To stop the signal magnetic field on apseudo-random-signal-wise basis:

[0162] For example, when the value is “−1” in a random sequence like anM-sequence consisting of unit periods T_(unit) of the same length N_(M),the signal magnetic field is turned ON, but when the value is “1,” thesignal magnetic field is turned OFF; and this sequence is repeated. Inthis case, the time average of the sequence is set to 0.

[0163]FIG. 24 shows temporal variations in the amplitude of the measuredmagnetic field in the case of the signal magnetic field being stopped bythe method (1). FIG. 25 shows temporal variations in the amplitude ofthe measured magnetic field in the case of the signal magnetic fieldbeing stopped by the method (2).

[0164] Next, as depicted in FIG. 26, the correlation function betweenthe sequence s(t) and the norm of the measured magnetic field or tireabsolute value of its particular component is calculated (S121, S122,S123). As the correlation function, it is possible to use any one ofthose calculated by $\begin{matrix}{{R(\tau)} = {\int_{t_{k}}^{t_{k} + {N_{T}T_{period}}}{{{H_{m}\left( {{r - r_{c}},\theta_{c},t} \right)}}\quad {s\left( {t - \tau} \right)}{{t}.}}}} & (43) \\{{R(\tau)} = {\int_{t_{k}}^{t_{k} + {N_{T}T_{period}}}{\sqrt{\left( {H_{m}\left( {{r - r_{c}},\theta_{c},t} \right)} \right)^{2}}{s\left( {t - \tau} \right)}{{t}.}}}} & (44) \\{{{R_{\alpha}(\tau)} = {\int_{t_{k}}^{t_{k} + {N_{T}T_{period}}}{{{H_{m,\alpha}\left( {{r - r_{c}},\theta_{c},t} \right)}}\quad {s\left( {t - \tau} \right)}{t}}}},{\alpha = x},y,{z.}} & (45) \\{{{R_{\alpha}(\tau)} = {\int_{t_{k}}^{t_{k} + {N_{T}T_{period}}}{\sqrt{\left( {H_{m,\alpha}\left( {{r - r_{c}},\theta_{c},t} \right)} \right)^{2}}{s\left( {t - \tau} \right)}{t}}}},{\alpha = x},y,{z.}} & (46)\end{matrix}$

[0165] in this case, the period for which to detect the correlation isset to an integral multiple N_(T)T_(period) of the period T_(period).

[0166] The OFF state of the signal magnetic field can be detected (S125)from the time τ=t_(sync) at which any one of the above correlationfunctions become maximum (S124). That is, a sequence s(t−t_(sync)),which starts at the time τ=t_(sync), is used, and when the sequence s(t)is “1,” the signal magnetic field is regarded as being OFF; in this way,the ON/OFF operation of the signal magnetic field is determined.

[0167] In the thus determined signal magnetic field OFF period thedirection of the measured magnetic field is detected, and the directionis regarded as the direction of the noise magnetic field (S126). Whenthe sequence s(t) is “−1” (a second numerical value), the signalmagnetic field is turned ON, and when the sequence is “1” (a firstnumerical value), the signal magnetic field is turned OFF; this sequenceis repeated in this way.

[0168] Sixth Method

[0169] As is the case with the filth method, the signal magnetic fieldis periodically stopped under control of such a predetermined procedureas described below.

[0170] (1) To stop the signal magnetic field on a rectangular-wave-wise:

[0171] The signal magnetic field is repeatedly turned ON and OFF withthe period T_(period), for instance. $\begin{matrix}\begin{matrix}{{{s(t)} = 1},} & {t_{k} \leq t < {t_{k} + {t_{stop}.}}} \\{\quad {{= {- 1}},}} & {{t_{k} + t_{stop}} \leq t \leq {t_{k + 1}.}}\end{matrix} & (41)\end{matrix}$

[0172] and when a sequence s(t) is 1, the signal magnetic field isturned OFF, but when the sequence is −1, die signal magnetic field isturned ON. In the above,

t _(k+1) −k _(k) =T _(period) , k=1, 2, 3,   (42)

[0173] (2) To stop the signal magnetic field on apseudo-random-signal-wise basis:

[0174] For example, when the value is “−1” in a random sequence like anM-sequence consisting of unit periods T_(unit) of the same length N_(M),the signal magnetic field is turned ON, but when the value is “1,” thesignal magnetic field is turned OFF; and this sequence is repeated.

[0175] In this case, the sequence s(t) is chosen so that it changes foreach predetermined time unit Δt_(unit). And, the time average of thesequence is “0.”

[0176] Next, as depicted in FIG. 27, the correlation function betweenthe sequence s(t) and the norm of the measured magnetic field or theabsolute value of its particular component is calculated (S131, S132,S133) as in case of the fifth method. As the correlation function, it ispossible to use any one of those calculated by $\begin{matrix}{{R(\tau)} = {\int_{t_{k}}^{t_{k} + {N_{T}T_{period}}}{{{H_{m}\left( {{r - r_{c}},\theta_{c},t} \right)}}\quad {s\left( {t - \tau} \right)}{{t}.}}}} & (43) \\{{R(\tau)} = {\int_{t_{k}}^{t_{k} + {N_{T}T_{period}}}{\sqrt{\left( {H_{m}\left( {{r - r_{c}},\theta_{c},t} \right)} \right)^{2}}{s\left( {t - \tau} \right)}{{t}.}}}} & (44) \\{{{R_{\alpha}(\tau)} = {\int_{t_{k}}^{t_{k} + {N_{T}T_{period}}}{{{H_{m,\alpha}\left( {{r - r_{c}},\theta_{c},t} \right)}}\quad {s\left( {t - \tau} \right)}{t}}}},{\alpha = x},y,{z.}} & (45) \\{{{R_{\alpha}(\tau)} = {\int_{t_{k}}^{t_{k} + {N_{T}T_{period}}}{\sqrt{\left( {H_{m,\alpha}\left( {{r - r_{c}},\theta_{c},t} \right)} \right)^{2}}{s\left( {t - \tau} \right)}{t}}}},{\alpha = x},y,{z.}} & (46)\end{matrix}$

[0177] In this case, the period for which to detect the correlation isset to an integral multiple N_(T)T_(period) of the period T_(period).

[0178] In this instance, there are present, in general, plural timesτ=t_(sync,k) (k=1, 2, . . . , N_(sync)) in which the correlationfunction becomes maximum and the maximum value exceeds a predeterminedvalue (S134). Assume, for example, that t_(sync,k), (k=1, 2, . . . ,N_(sync)) is an arrangement of such times in order of time. When thecorrelation value between the sequence s(t) and the signal magneticfield is appropriate,

Δt _(sync, k) ^(=t) _(sync, k) −k _(sync, l) , k=2, . . . , N_(sync).  (47)

[0179] is virtually an integral multiple of the time unit Δt_(unit).Then, the average of the value resulting from the subtraction of anintegral multiple M_(sync,k)Δt_(unit) of the time unit Δt_(sync), wherek=2, . . . , N_(sync, k), from Δt_(sync,k), where k=2, . . . , N_(sync),is calculated by $\begin{matrix}{{\delta \quad t_{{syn}\quad c}} = {\frac{\sum\limits_{k = 2}^{N_{sync}}\left( {{\Delta \quad t_{{sync},k}} - {M_{{sync},k}\Delta \quad t_{unit}}} \right)}{N_{sync} - 1}.}} & (48)\end{matrix}$

[0180] In this case,

t _(sync) =t _(sync, l) +δt _(sync)  (49)

[0181] provides the beginning of the sequence signal corresponding tothe ON/OFF operation of the signal magnetic field.

[0182] Accordingly, the period during which the signal magnetic field isOFF can easily be set based on the sequence s(t−t_(sync)).

[0183] By applying the same method as the first method to the magneticfield vector H_(m)(r−r_(c), θ_(c), t) measured in this period, thedirection e_(n)(r) of the noise magnetic field vector H_(n)(r, t) can becalculated (S138).

[0184] Seventh Method

[0185] This method will be described below with reference to FIGS. 28,29, 30 and 31.

[0186] As is the case with the fifth1 method, the signal magnetic fieldis periodically stopped, for example, by such a procedure as describedbelow.

[0187] (1) To stop the signal magnetic field on a rectangular-wave-wise:

[0188] The signal magnetic field is repeatedly turned ON and OFF withthe period T_(period), for instance. $\begin{matrix}\begin{matrix}{{{s(t)} = 1},} & {t_{k} \leq t < {t_{k} + {t_{stop}.}}} \\{\quad {{= {- 1}},}} & {{t_{k} + t_{stop}} \leq t \leq {t_{k + 1}.}}\end{matrix} & (41)\end{matrix}$

[0189] and when a sequence s(t) is 1, the signal magnetic field isturned OFF, but when the sequence is −1, the signal magnetic field isturned ON. In the above,

k _(k+1) −t _(k) =T _(period) , k=1, 2, 3,   (42)

[0190] (2) To stop the signal magnetic field on apseudo-random-signal-wise basis:

[0191] For example, when the value is “−1” in a random sequence like anM-sequence consisting of unit periods T_(unit) of the same length N_(M),the signal magnetic field is turned ON, but when the value is “1,” thesignal magnetic field is turned OFF; and this sequence is repeatedaccordingly In this case, the time average of the sequence is “0.”

[0192] Next, the correlation function between the sequence s(t) and themeasured magnetic field H_(m)(r−r_(c), θ_(c), t) is calculated (S141,S142, S143). The period T_(period) is divided into equally spacedN_(div) sections of a length T_(div), and either one of the followingcalculations is conducted. $\begin{matrix}{{{R_{\alpha}\left( t_{k} \right)} = {\int_{t_{k}}^{t_{k} + T_{period}}{{{H_{m,\alpha}\left( {{r - r_{c}},\theta_{c},t} \right)}}\quad {s\left( {t - t_{k}} \right)}{t}}}},{k = 1},\quad \ldots \quad,{N_{div};{\alpha = x}},y,{z.}} & (50) \\{{{R_{\alpha}\left( t_{k} \right)} = {\int_{t_{k}}^{t_{k} + T_{period}}{\sqrt{\left( {H_{m,\alpha}\left( {{r - r_{c}},\theta_{c},t} \right)} \right)^{2}}{s\left( {t - t_{k}} \right)}{t}}}},{k = 1},\quad \ldots \quad,{N_{div};{\alpha = x}},y,{z.}} & (51)\end{matrix}$

[0193] In this case, a symbol R_(α)(t_(k)), where α=x, y, z and k=1, . .. , N_(div), is the time correlation between an α componentH_(m,α)(r−r_(c), θ_(c), t) of the measured magnetic field H_(m)(r−r_(c),θ_(c), t) and the sequence s(t). And

t _(k) =t ₀ +k˜T _(div) , k=1, . . . , N _(div).  (52)

[0194] The measured magnetic field may also be correlated with the timethat is an m-multiple of the period T_(period). That is, $\begin{matrix}{{{R_{\alpha}\left( t_{k} \right)} = {\int_{t_{k}}^{t_{k} + {m\quad T_{period}}}{{{H_{m,\alpha}\left( {{r - r_{c}},\theta_{c},t} \right)}}\quad {S_{m\quad p}\left( {t - t_{k}} \right)}{t}}}},{k = 1},\quad \ldots \quad,{N_{div};{\alpha = x}},y,{z.}} & (53) \\{{{R_{\alpha}\left( t_{k} \right)} = {\int_{t_{k}}^{t_{k} + {m\quad T_{period}}}{\sqrt{\left( {H_{m,\alpha}\left( {{r - r_{c}},\theta_{c},t} \right)} \right)^{2}}{S_{m\quad p}\left( {t - t_{k}} \right)}{t}}}},{k = 1},\quad \ldots \quad,{N_{div};{\alpha = x}},y,{z.}} & (54)\end{matrix}$

[0195] In this instance, the sequence s(t) is replaced with S_(mp)(t),where

S _(mp)(t)=S(t+T _(period)),

S _(mp)(t)=s(t), 0≦t≦T _(period).  (55)

[0196] This is followed by calculating the component H_(m) ^(p)(r−r_(c),θ_(c), t_(k), t), where k=1, . . . , N_(div), of the measured magneticfield H_(m)(r−r_(c), θ_(c), t) projected in the vector

e _(n)(t _(k))=(R _(x)(t _(k)), R _(y)(t _(k)), R _(z)(t _(k))), wherek=1, . . . ,N _(div)

[0197] formed by correlation functions R_(α)(t_(k)), where α=x, y, z,corresponding to the respective components x, y and z of the measuredmagnetic field H_(m)(r−r_(c), θ_(c), t). Here, a symbol t_(k) containedas a variable of the projective component indicates that the projectivecomponent depends on the variable t_(k).

[0198] In this method, the vector e_(n)(t_(k)) can be used as thedirection of the noise magnetic field through utilization of the timet_(k) in which a fluctuation in the absolute value of the projectivecomponent vector H_(m)(r−r_(c), θ_(c), t_(k), t), where k=1, . . . ,N_(div), $\begin{matrix}{{{{var}\left( t_{k} \right)} = \frac{\sqrt{{\langle\left( {{H_{m}^{P}\left( {{r - r_{c}},\theta_{c},t_{k},t} \right)} - {\langle{{H_{m}^{P}\left( {{r - r_{c}},\theta_{c},t_{k},t} \right)}}\rangle}_{t}} \right)^{2}\rangle}_{t}}}{{\langle{{H_{m}^{P}\left( {{r - r_{c}},\theta_{c},t_{k},t} \right)}}\rangle}_{t}}},{k = 1},\quad \ldots \quad,{N_{div}.}} & (56)\end{matrix}$

[0199] becomes minimum or smaller than a predetermined value (S145 a).in the above z,900 .z,901 _(t) means the calculation of the timeaverage.

[0200] Further, variances of the x-component H_(m,x)(r−r_(c), θ_(c),t_(k), t), y-component H_(m,y)(r−r_(c), θ_(c), t_(k), t) and z-componentH_(m,z)(r−r_(c), θ_(c), t_(k), t) of the projective component vectorH_(m)(r−r_(c), θ_(c), t_(k), t), where k=1, . . . , N_(div),$\begin{matrix}{{{{var}_{\alpha}\left( t_{k} \right)} = \frac{\sqrt{{\langle\left( {{H_{m,\alpha}^{P}\left( {{r - r_{c}},\theta_{c},t_{k},t} \right)} - {\langle{{H_{m,\alpha}^{P}\left( {{r - r_{c}},\theta_{c},t_{k},t} \right)}}\rangle}_{t}} \right)^{2}\rangle}_{t}}}{{\langle{{H_{m}^{P}\left( {{r - r_{c}},\theta_{c},t_{k},t} \right)}}\rangle}_{t}}},{\alpha = x},y,{z;{k = 1}},\quad \ldots \quad,{N_{div}.}} & (57)\end{matrix}$

[0201] are calculated, and the vector e_(n)(t_(k)) can be used as thedirection of the noise magnetic field through utilization of the timet_(k) in which the sum of the above-mentioned variances $\begin{matrix}{{\sum\limits_{{\alpha = x},y,z}{{var}_{\alpha}\left( t_{k} \right)}}{or}} & (58) \\{\sqrt{\sum\limits_{{\alpha = x},y,z}\left( {{var}_{\alpha}\left( t_{k} \right)} \right)^{2}}.} & (59)\end{matrix}$

[0202] becomes minimum or smaller than a predetermined value (S145 b).In this case, there is the possibility that the correlation functionsR_(x)(t_(k)), R_(y)(t_(k)) and R_(z)(t_(k)) at a certain time t_(k) havelost their original signs. Hence, it is necessary to evaluate thefluctuation of the projective component at each time t_(k) for fourcombinations [R_(x)(t_(k)), R_(y)(t_(k)), R_(z)(t_(k))], [R_(x)(t_(k)),R_(y)(t_(k)), −R_(z)(t_(k))], [R_(x)(t_(k)), −R_(y)(t_(k)),R_(z)(t_(k))] and [R_(x)(t_(k)), −R_(y)(t_(k)), −R_(z)(t_(k))].

[0203] Further, the period during which the signal magnetic field is OFFcan easily be set (S145 c, S145 d) based on the sequence s(t−t_(k)). Byapplying the same method as the first one to the magnetic field vectorH_(n)(r−r_(c), θ_(c), t) measured in this period, the direction e_(n)(r)of the noise magnetic field vector H_(n)(r, t) can be obtained (S146).In the above, use is made of the time t_(k) of the equally spacedN_(div) sections of a the time length T_(div) divided from the periodT_(period), but it is also possible to use the time when the correlationfunction given by Eq. (45) or (46) becomes maximum or when thecorrelation function becomes maximum and exceeds a predetermined value.

[0204] Method for Determining the Direction of the Noise Magnetic Fieldwhen the Number of Noise Magnetic Fields is Virtually Two

[0205] Even in a case of two noise magnetic fields, when a first one ofthe two noise magnetic fields has far higher al intensity than thesecond noise magnetic field at a first frequency and the second noisemagnetic field has far higher an intensity than the first noise magneticfield at the second frequency, the directions of the first and secondnoise magnetic field can easily be calculated through utilization ofthese frequency components in the measured magnetic field.

[0206] If the first or second frequency is close to the frequency of thesignal magnetic field, the directions of the noise magnetic fieldscan,be determined from the measured magnetic field having passed througha band pass filter that permits the passage therethrough of onlyfrequencies near those of the signal magnetic field, by the same methodas the fourth or fifth method for use in the case of virtually one noisemagnetic field.

[0207] When either of the first and second frequencies does not equal tothe frequency of the signal magnetic field, the directions of therespective noise magnetic fields need only to be calculated by the samemethod as the first one for use in the case of virtually one noisemagnetic field.

OTHER EMBODIMENTS

[0208] The present invention is also effective when the signal magneticfield generated by the magnetic field source is virtually axiallysymmetric, and the invention permits position determination with asmaller number of magnetic sensors or by magnetic field sensing at asmaller number of positions than in the case of a magnetic field of lowsymmetry.

[0209] Further, when only one noise magnetic field affects themeasurement of the digging position and the tilt angle of the magneticfield source is known which is an inclination of the axis of symmetrycorresponding to the axial direction of the signal magnetic field set inthe magnetic field source with respect to the vertical direction, theprojective component of the magnetic field, measured at each of two ormore different positions, on a plane perpendicular to die direction ofthe noise magnetic field sensed at each of the magnetic field sensingpositions is calculated the position of the magnetic field source andits azimuth angle that is the direction of the axis of symmetry in ahorizontal plane can be calculated from the above-said projectivecomponent.

[0210] Further, according to this invention method, when virtually onenoise magnetic field affects the measurement of the digging position,the projective component of the magnetic field, measured at each ofthree or more different positions, on a plane perpendicular to thedirection of the noise magnetic field sensed at each of the magneticfield sensing positions is calculated; the position of the magneticfield source, its tilt angle that is an inclination of the axis ofsymmetry corresponding to the axial direction of the signal magneticfield set in the magnetic field source with respect to the verticaldirection, and the azimuth angle of the magnetic field source that islie direction of the axis of symmetry in the horizontal plane can becalculated from the above-said projective component.

[0211] Further, when virtually two noise magnetic fields alone affectthe measurement of the digging position and the tilt angle of themagnetic field source is known which is an inclination of the axis ofsymmetry corresponding to the axial direction of the signal magneticfield set in the magnetic field source with respect to the verticaldirection, the projective component of the magnetic field, measured ateach of four or more different positions, on a straight lineperpendicular to both of the direction of a first one of the two noisemagnetic fields sensed at each magnetic field sensing position and thedirection of the remaining second noise magnetic field sensed at thesame position is calculated; the position of the magnetic field sourceand its azimuth angle that is the direction of the axis of symmetry inthe horizontal plane can be calculated from the above-said projectivecomponent.

[0212] Further, when virtually two noise magnetic fields alone affectthe measurement of the digging position, the projective component of themagnetic field, measured at each of five or more different positions, ona straight line perpendicular to both of the direction of a first one ofthe two noise magnetic fields sensed at each magnetic field sensingposition and the direction of the remaining second noise magnetic fieldsensed at the same position is calculated; the position of the magneticfield source, its tilt angle that is an inclination of the axis ofsymmetry corresponding to the axial direction of the signal magneticfield set in the magnetic field source with respect to the verticaldirection, and the azimuth angle that is the direction of the axis ofsymmetry in the horizontal plane can be calculated from the above-saidprojective component.

[0213] Moreover, when virtually two noise magnetic fields alone affectthe measurement of the digging position, the frequency component of afirst one of the two noise magnetic fields, in the vicinity of which theremaining second noise magnetic field and the signal magnetic field havesubstantially no frequency components, is measured to thereby permitdetection of the direction of the first noise magnetic field in terms ofvector; and the frequency component of the second noise magnetic fields,in the vicinity of which the first noise magnetic field and the signalmagnetic field have substantially no frequency components, is measuredto thereby permit detection of the direction of the second noisemagnetic field in terms of vector.

[0214] In the present invention, it is effective to use, as a magneticsensor, a three-axis magnetic sensor that senses three magnetic fieldsorthogonal to one another at substantially the same position.

[0215] The magnetic sensor for use in die present invention may be anykinds of sensors as long as they are capable to three magnetic fieldsorthogonal to one another at substantially the same position, but thethree-axis magnetic sensor is suitable which senses three magneticfields orthogonal to one another at substantially the same position.Alternatively, it is possible that one magnetic sensor capable ofsensing a magnetic field in only one direction is tuned at the sameposition toward three orthogonal directions one after another to sensethe three orthogonal magnetic fields.

[0216] In carrying out the present invention, it is possible to employsuch a frame 12 as depicted in FIG. 32 which has magnetic sensor fixingmeans 11 mounted thereon to fix three-axis magnetic sensors and a tiltangle gauge 13 for detecting the inclination of the frame with respectto a vertical direction. The position of each magnetic sensor fixingmeans on the frame is known, and the magnetic sensor fixing meanspossesses a function of fixing the magnetic sensor in a predeterminedorientation to the frame. The magnetic sensor fixing means 11 isprovided with, for example, three faces orthogonal to one another, andhas a mechanism that fixes the magnetic sensor at a predetermined anglewhen a predetermined !ace of the sensor case is pressed against any oneof tie three faces of the sensor fixing means. One magnetic sensor orone three-axis magnetic sensor is fixed to these magnetic sensor fixingmeans one after another to sense the magnetic fields.

[0217] In another alternative, a plurality of magnetic sensors may befixed in predetermined orientations to the frame 12 at a plurality ifpositions to simultaneously sense magnetic fields at the plurality ofpositions.

[0218] As described above, tile present invention employs a frameprovided with a plurality of magnetic sensor fixing means each capableof removably or fixedly mounting a three-axis magnetic sensor and a tiltangle sensor capable of detecting the tilt angle of an orthogonalcoordinate system to the vertical direction, the magnetic fixing meansbeing mounted on the frame so that their positions and orientations areknown; the magnetic sensor is removably or fixedly mounted on a requirednumber of magnetic sensor fixing means to sense magnetic fields, and thetilt angle of the frame during magnetic field sensing and theorientation of the magnetic sensor at each magnetic sensor mountingposition with respect to the frame are used to calculate From themagnetic field. sensed at each magnetic sensor mounting position thesensed magnetic field, a noise magnetic field and a signal magneticfield as vectors in a coordinate system fixed to the ground.

[0219] The magnetic field generating means for tile signal magneticfield in the present invention may be a coil. The magnetic fieldgenerating means may be one electric wire as well, or may also be oneelectric wire that is straight only in the vicinity of the place ofposition determination.

[0220] As described above, even if a buried power line, railroad tracks,or similar noise magnetic sources are present near a construction site,the present invention permits highly reliable position determinationwithout being affected by noise magnetic fields generated by such noisemagnetic field sources.

[0221] The present invention is intended for measuring the diggingposition in the non-open-cut method of excavation, but is applicable aswell to many technical fields that involve position determination bysensing magnetic fields.

What I claim is:
 1. A digging position determining method for anon-open-cut method of excavation, comprising the steps of: sensing anAC magnetic field provided from a magnetic field source by anabove-ground magnetic sensor and calculates the position of the magneticfield source from the magnitude and direction of the sensed magneticfield, when there is present, in addition to a signal magnetic fieldgenerated by said magnetic field source, a noise magnetic fieldgenerated by a nearby current, and calculating at lease one of theposition of said magnetic field source, the tilt angle of said magneticfield source to the vertical direction and the azimuth of said magneticfield source that is its axial direction in a horizontal plane; throughusing a projective component of said magnetic field, sensed by saidmagnetic sensor, on a plane or straight line orthogonal to avector-valued direction of said noise magnetic field, of using a signalmagnetic field component obtained by synchronous detection of aloriginal sensed magnetic field through utilization of said projectivecomponent as a reference signal.
 2. A digging position determiningmethod according to claim 1, characterized in that a vector-valueddirection of said noise magnetic field is detected prior to the positiondetermination in the absence of any nearby magnetic field source.
 3. Adigging position determining method according to claim 1, characterizedin that a vector-valued direction of the frequency component of saidnoise magnetic field different from the frequency component of saidsignal magnetic field is detected and is regarded as a vector-valueddirection of a noise magnetic field of the same frequency component asthat of said signal magnetic field.
 4. A digging position determiningmethod according to claim 3, characterized in that: a vector-valueddirection of the frequency component of each sensed magnetic fielddifferent from the frequency component of said signal magnetic field iscalculated; and a vector-valued direction of the frequency component ofsaid noise magnetic field, at which a fluctuation in the amplitude ordirection of a projective component of said sensed magnetic field on aplane or line orthogonal to said vector-valued direction of said sensedmagnetic field becomes minimum or smaller than a predetermined value, isregarded as a vector-valued direction of said noise magnetic field ofthe same frequency component as that of said signal magnetic field.
 5. Adigging position determining method according to claim 4, characterizedin that: a vector-valued direction of a line spectrum component of saidnoise magnetic field of a frequency component different from that ofsaid signal magnetic field is calculated; and a vector-valued directionof the line spectrum component of said noise magnetic field, at which afluctuation in the amplitude or direction of a projective component ofsaid sensed magnetic field on a plane or line orthogonal to saidvector-valued direction of said noise magnetic field becomes minimum orsmaller than a predetermined value, is regarded as a vector-valueddirection of said noise magnetic field of the same frequency componentas that of said signal magnetic field.
 6. A digging position determiningmethod according to claim 1, characterized in that: said signal magneticfield is turned OFF by a predetermined procedure; the. OFF period ofsaid signal magnetic field is estimated; and the direction of saidsensed magnetic field during said OFF period is regarded as saidvector-valued direction of said noise magnetic field.
 7. A diggingposition determining method according to claim 6, characterized in that:a decrease in the intensity of said sensed magnetic field is detected tothereby estimate the OFF period of said signal magnetic field.
 8. Adigging position determining method according to claim 6, characterizedin that: said signal magnetic field is periodically turned OFF by apredetermined procedure; a time correlation function in a finite periodis calculated between a sequence, which takes a first numerical valueduring the OFF period of said signal magnetic field and a second numeralvalue different from said first value during an ON period of said signalmagnetic field and is a time function of a “0” time average, and theabsolute value of said sensed magnetic field or square root of saidabsolute value, or the absolute value of each vector-valued component ofsaid sensed magnetic field or square root of said absolute value; and aperiod is set during which said signal magnetic field is held OFF bysaid sequence that maximizes and minimizes said time correlationfunction when said first numerical value is larger than said secondnumerical value and minimizes said time correlation function when saidfirst numerical value is smaller than said second numerical value, andthe direction of said sensed magnetic field in said period is regardedas the direction of said noise magnetic field.
 9. A digging positiondetermining method according to claim 6, characterized in that: saidsignal magnetic Field is periodically turned OFF by a predeterminedprocedure; said signal magnetic field is turned ON and OFF with apredetermined period following a sequence that takes a fast numericalvalue during the OFF period of said signal magnetic field and a secondnumeral value different from said first value during an ON period ofsaid signal magnetic field and is a time function of a “0” time average;a time correlation function in a finite period is calculated betweensaid sequence and the absolute value of said sensed magnetic field orsquare root of said absolute value, or the absolute value of eachvector-valued component of said sensed magnetic field or square root ofsaid absolute value; a plurality of starting times of said sequence,which maximizes said time correlation function in excess of apredetermined value when said first numerical value is larger than saidsecond numerical value and minimizes said time correlation function whensaid first numerical value is smaller than said second numerical value,is set; the first one of said plurality of starting times is subtractedfrom the remaining other starting times to obtain the time differenceand an average value of said remaining starting times except an integralmultiple of a period closest to said time difference is calculated; anda period is set during which said signal magnetic field is held OFF by asequence whose starting time is the sum of said average value and saidfirst starting time, and the direction of said sensed magnetic fieldduring said period is regarded as the direction of said noise magneticfield.
 10. A digging position determining method according to claim 6,characterized in that: said signal magnetic field is periodically turnedOFF by a predetermined procedure; a time correlation function in afinite period is calculated be*ween a sequence, which takes a firstnumerical value during the OFF period of said signal magnetic field anda second numeral value different from said first value during an ONperiod of said signal magnetic field and is a time function of a “0”time average, and the absolute value of each vector-valued component ofsaid sensed magnetic field or a square root of said absolute value; andthe direction of a vector formed by said three time correlationfractions, in which a fluctuation in the amplitude or direction of aprojective component of said sensed magnetic field on a plane. or lineorthogonal to the direction of said vector becomes minimum, is regardedas the direction of said noise magnetic field.
 11. A digging positiondetermining method according to claim 6, characterized in that: saidsignal magnetic field is periodically turned OFF by a predeterminedprocedure; a period longer than the period for which said signalmagnetic field is held OFF is divided into time intervals shorter thansaid signal magnetic field OFF period, and a vector-valued direction ofsaid sensed magnetic field during each of said time intervals isdetected; and a vector-valued direction of said each time interval, inwhich a fluctuation in the amplitude or direction of a projectivecomponent of said sensed magnetic field on a plane or line orthogonal toa vector-valued direction of said sensed magnetic field in said eachtime interval becomes minimum, is regarded as a vector-valued directionof said noise magnetic field.
 12. A digging position determining methodaccording to claim 6, characterized in that: said signal magnetic fieldis periodically turned OFF by a predetermined procedure; timecorrelation functions in a finite period are calculated between asequence, which takes a first numerical value during the OFF period ofsaid signal magnetic field and a second numeral value different fromsaid first value during an ON period of said signal magnetic field andis a time function of a “0” time average, and the absolute values ofthree vector-valued components of said sensed magnetic field or squareroots of said absolute values; and the time for executing one round ofsaid sequence is divided into tine intervals shorter than said signalmagnetic field OFF period, and a vector-valued direction of each of saidtime intervals, in which a fluctuation in the amplitude or direction ofa projective component of said sensed magnetic field on a plane or lineorthogonal to vectors of three components of said time correlationfunctions becomes minimum at a representative time of said each timeinterval, is regarded as a vector-valued direction of said noisemagnetic field.
 13. A digging position determining method according toclaim 1, characterized in that said signal magnetic field generated bysaid magnetic field source is virtually symmetrical with respect to oneaxis of symmetry.
 14. The digging position determining method as claimedin claim 13, characterized in that: when the number of noise magneticfields affecting the digging position determination is virtually onlyone and the tilt angle of said magnetic field source is known which isan inclination of the axis of symmetry corresponding to the axialdirection of said signal magnetic field set in said magnetic fieldsource with respect to the vertical direction, a projective component ofa magnetic field, sensed at each of two or more different positions, ona plane orthogonal to the direction of said noise magnetic field sensedat each of said magnetic field sensing positions is calculated; and theposition of the magnetic field source and the azimuth angle of saidmagnetic field source that is the direction of said axis of symmetry ina horizontal plane are calculated from said projective component or asignal magnetic field component obtained by synchronous detection of theoriginal sensed magnetic field through the use of said projectivecomponent as a reference signal.
 15. A digging position determiningmethod according to claim 1, characterized in that: when the number ofnoise magnetic fields affecting the digging position determination isvirtually only one, a projective component of a magnetic field, sensedat each of three or more different positions, on a plane orthogonal tothe direction of said noise magnetic field sensed at each of saidmagnetic field sensing positions is calculated; and the position of themagnetic field source, the tilt angle of said magnetic field source thatis an inclination of the axis of symmetry corresponding to the axialdirection of said signal magnetic field set in said magnetic fieldsource with respect to the vertical direction, and the azimuth angle ofsaid magnetic field source that is the direction of said axis ofsymmetry in a horizontal plane are calculated from said projectivecomponent or a signal magnetic field component obtained by synchronousdetection of the original sensed magnetic field through the use of saidprojective component as a reference signal.
 16. A digging positiondetermining method according to claim 1, characterized in that: when thenumber of noise magnetic fields affecting the digging positiondetermination is virtually only one mid the tilt angle of said magneticfield source is known which is an inclination of the axis of symmetrycorresponding to the axial direction of said signal magnetic field setin said magnetic field source with respect to the vertical direction, aprojective component of said magnetic field, sensed at each of four ormore different positions, on a plane orthogonal to the directions of-both first and second noise magnetic fields sensed at each of saidmagnetic field sensing positions is calculated; and the position of themagnetic field source and the azimuth angle of said magnetic fieldsource that is the direction of said axis of symmetry in a horizontalplane are calculated from said projective component or a signal magneticfield component obtained by synchronous detection of the original sensedmagnetic field through the use of said projective component as areference signal.
 17. A digging position determining method according toclaim 1, characterized in that: when the number of noise magnetic fieldsaffecting the digging position determination is virtually only first andsecond noise magnetic fields, a projective component of said magneticfield, sensed at each of four or more different positions, on a planeorthogonal to the directions of both said first and second noisemagnetic fields sensed at each of said magnetic field sensing positionsis calculated; and the position of the magnetic field source, the tiltangle of said magnetic field source that is an inclination of the axisof symmetry corresponding to the axial direction of said signal magneticfield set in said magnetic field source with respect to the verticaldirection, and the azimuth angle of said magnetic field source that isthe direction of said axis of symmetry in a horizontal plane arecalculated from said projective component or a signal magnetic fieldcomponent obtained by synchronous detection of the original sensedmagnetic field through the use of said projective component as areference signal.
 18. A digging position determining method according toclaim 1, characterized in that: when the number of noise magnetic fieldsaffecting the digging position determination is virtually only first andsecond noise magnetic fields, the frequency component of said firstnoise component, around which said second noise magnetic field and saidsignal magnetic field have substantially no frequency components, aremeasured to thereby obtain a vector-valued direction of said first noisemagnetic field, and the frequency component of said second noisecomponent, around which said first noise magnetic field and said signalmagnetic field have substantially no frequency components, are measuredto thereby obtain a vector-valued direction of said second noisemagnetic field.
 19. A digging position determining method according toclaim 1, characterized in that said magnetic sensor is a three-axismagnetic sensor that senses magnetic fields of three axial directionsorthogonal to one another at substantially the same position.
 20. Adigging position determining method according to claim 19, characterizedin that: a frame is used which is provided with magnetic sensor fixingmeans for removably or fixedly mounting said three-axis magnetic sensor;and said frame is provided with a tilt angle sensor fixed to said frame,for sensing the tilt angle of an orthogonal coordinate system to avertical direction; wherein: other magnetic fields are sensed by saidthree-axis magnetic sensor removably or fixedly mounted on each of arequired number of magnetic sensor fixing means that are mounted on saidframe so that the position and orientation of said magnetic sensorfixing means with respect to said frame are known; and the tilt angle ofsaid frame at the time of sensing said other magnetic fields and theorientation of said three-axis magnetic sensor at each three-axismagnetic sensor mounting position with respect to said frame are used tocalculate said sensed magnetic field, said noise magnetic field and saidsignal magnetic field as vectors in a coordinate system fixed to theground from said other magnetic fields sensed at said each three-axismagnetic sensor mounting position.
 21. A digging position determiningmethod according to claim 19, characterized in that said other magneticfields are sensed by said three-axis magnetic sensor fixed at each of arequired number of magnetic sensor mounting positions.
 22. A diggingposition determining method according to claim 19, characterized in thatmagnetic fields are sensed by one three-axis magnetic sensor that isremovably mounted at said required number of magnetic sensor mountingpositions one after another.
 23. A digging position determining methodaccording to claim 1, characterized in that said magnetic fieldgenerating means is a coil.
 24. A digging position determining methodaccording to claim 1, characterized in that said magnetic fieldgenerating means ant electric wire.
 25. A digging position determiningmethod according to claim 1, characterized in that said magnetic fieldgenerating means is a straight electric wire disposed in the vicinity ofthe magnetic field sensing position.